Vibrational energy level statistics of small molecules

A simple model Hamiltonian including kinetic coupling of adjacent bonds is chosen for investigations of the statistics of vibrational eigenenergies for a series of three- and four-atomic molecules. Depending on the coupling strength which is governed by structural characteristics of each molecule, the systems can be assigned to one of the two universal types of statistical behavior observed for energy levels: level clustering or level repulsion. Although the model is simple, the statistical measures are still sensitive enough to reveal significant differences between the molecules. These results are discussed in terms of the individual structural properties such as bond angles and atomic masses.